CN108090323B - Wind power curve fitting method based on infinite mixed Gauss and spline regression - Google Patents

Wind power curve fitting method based on infinite mixed Gauss and spline regression Download PDF

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CN108090323B
CN108090323B CN201810023362.0A CN201810023362A CN108090323B CN 108090323 B CN108090323 B CN 108090323B CN 201810023362 A CN201810023362 A CN 201810023362A CN 108090323 B CN108090323 B CN 108090323B
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胡清华
汪运
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Tianjin University
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Abstract

The invention discloses a wind power curve fitting method based on infinite mixed Gauss and spline regression, which comprises the steps of preprocessing data, constructing a robust spline regression model, optimizing the robust spline regression model by using variational Bayes, and obtaining a power curve and a probability power curve.

Description

Wind power curve fitting method based on infinite mixed Gauss and spline regression
Technical Field
The invention relates to the field of new energy and the field of machine learning, in particular to a wind power curve fitting method based on infinite mixed Gauss and spline regression.
Background
Currently, with the global energy crisis and the increasingly severe environmental problems caused by the use of traditional energy sources such as coal and oil, the task of finding a substitute for the original traditional energy sources is becoming more urgent. Wind power has received increasing attention as a clean, renewable energy source. The large-scale wind power integration can relieve the energy crisis to a certain extent, and can bring economic benefits and reduce and relieve pollution. However, due to the randomness and intermittency of wind power, the completeness and stability of the whole power system are greatly influenced after large-scale wind power integration. Therefore, from the perspective of wind power integration, accurate power forecasting is necessary, and the operating cost of the power system can be reduced.
Since the relationship between wind speed and power can be represented by a power curve. Therefore, wind power forecasting is usually carried out by a two-step method, wherein a forecasting value of wind speed is obtained firstly in the first step, and power forecasting is obtained by utilizing a power curve in the second step. Typically, the power curve is provided by the manufacturer of the wind turbine. However, the power curve is a theoretical power curve, and the influence of factors such as environment (such as air temperature and humidity) is not considered. In practice, the actual power curve varies with the geographical environment and climate. Therefore, directly using the theoretical power curve to realize the power prediction brings extra prediction error. Therefore, many scholars also study how to obtain an accurate actual power curve to further improve the accuracy of wind power forecasting. Besides, the accurate power curve can also monitor the running state of the fan on line and reduce the running and maintenance cost of the fan and the like.
Currently, wind power curve modeling techniques can be divided into two broad categories: parametric models and non-parametric models. Generally, the parametric model is mainly composed of a mathematical expression with several parameters, and mainly includes a linear segmentation method, a polynomial power curve, an ideal power curve, a probability model, a dynamic power curve, a 4-parameter and 5-parameter logistic model, a modified hyperbolic tangent model, and the like. For polynomial models, cubic power curves, quadratic power curves, 6 th and 9 th order polynomial models are commonly used to fit the power curves. A disadvantage of parametric models is their limited performance in describing the dynamics of the power curve. Unlike parametric models, non-parametric models fit a variety of power curves using only historical power and wind speed data without using mathematical expressions and without prior knowledge of the shape of the power curve. The nonparametric model mainly comprises spline regression, an artificial neural network method, a fuzzy method and some data mining methods such as a support vector machine, a random forest, K nearest neighbor and the like. Although non-parametric models are more flexible than parametric models, they are also relatively computationally expensive.
In addition to the modeling of the power curve, another factor that affects us in obtaining an accurate power curve is the quality of the data. However, in practice, there are often many inconsistent samples in the obtained wind speed and power data. The reasons for the above phenomena include sensor errors, shutdown maintenance, wind abandonment and electricity limitation, and environmental factors such as icing. The characteristic of the inconsistent sample is that given a wind speed, the true power data is far from the power curve. In order to improve the quality of data, it is common to remove these inconsistent samples in advance and then use the processed data to construct a power curve model. However, a drawback of such methods is that we cannot guarantee that all inconsistent samples are detected.
When some non-uniform samples exist in the data, the actual power is far away from the power on the power curve, so that the error is large, the error distribution has a non-Gaussian characteristic, and the long tail phenomenon exists. In this case, the gaussian distribution hardly describes the error distribution of the above characteristics. However, some current models such as spline regression, polynomial models, etc. assume that the error follows gaussian distribution, and when some non-uniform samples exist in the training data, the real error distribution characteristics are not consistent with the assumed error distribution. Thus, in the presence of non-uniform samples, it is not appropriate to assume that the error follows a gaussian-distributed power curve model.
Disclosure of Invention
The invention aims to solve the technical problems of low precision and large error of the existing wind power curve, and provides a wind power curve fitting method based on infinite mixed Gauss and spline regression.
The technical scheme adopted by the invention for solving the technical problems is as follows:
a wind power curve fitting method based on infinite mixed Gauss and spline regression comprises the following steps:
1) data preprocessing:
drawing an empirical power curve according to actual wind speed and power data, removing obvious abnormal data, and representing a processed sample as
Figure GDA0002486166790000021
X is as describedi，yiRespectively representing wind speed and power value, and N represents the length of a training sample;
2) constructing a robust spline regression model:
constructing a robust spline regression model yi＝Zi(xi)β+eiZ of saidi(xi) Representing the input vector calculated from the spline basis, β representing the regression coefficient, eiRepresenting the regression error obeying an infinite mixture gaussian model:
Figure GDA0002486166790000022
said
Figure GDA0002486166790000031
Representing the variance of the kth Gaussian distribution, said regression coefficients β obeying a Gaussian distribution, said pikA weight value representing the k-th gaussian distribution,
Figure GDA0002486166790000032
and pikIs about
Figure GDA00024861667900000311
Is expressed as
Figure GDA0002486166790000033
Said parameters
Figure GDA0002486166790000034
Is a variable satisfying a Beta distribution with a parameter v
Figure GDA0002486166790000035
Figure GDA0002486166790000036
The hyperparameter v satisfies the parameter e0、f0Gamma distribution of (v ═ Gamma (ve | e))0，f0) Said e is0、f0Is set to 0.0001 and updates e according to the posterior distribution of the parameters obtained by variational bayes0、f0A value of (d);
3) and (3) optimizing a robust spline regression model by using variational Bayes:
constructing a final likelihood function according to prior distribution of each parameter in the robust spline regression model in the step 2):
Figure GDA0002486166790000037
p (-) is the probability distribution of the variable;
order to
Figure GDA0002486166790000038
According to the principle of variational Bayes, the posterior distribution of all parameters in the robust spline regression model is solved,
Figure GDA0002486166790000039
the < > is an expected operation;
4) and (3) obtaining a power curve and a probability power curve:
giving a new sample (x) based on the posterior distribution of the parameters obtained in step 3)*，y*) X is said*、y*Respectively representing the unknown wind speed value and the real power to be predicted, y is deduced by the following formula*Probability distribution of (2):
Figure GDA00024861667900000310
the muβ、ΣβRespectively representing the expectation and variance, Z, in the posterior distribution of the parameter β*Expressed is the sum of the wind speed x calculated according to the spline base*Corresponding input vector, y*The predicted distribution of (a) is a Gaussian mixture model, said Z*μβIs y*The point prediction value of (1);
according to y ═ Z (x) muβObtaining a predicted power curve;
and solving a corresponding probability power curve according to the probability distribution corresponding to each predicted value.
The invention has the following beneficial effects: the wind power curve fitting method can fit any complex distribution theoretically due to the adoption of infinite mixed Gaussian distribution, so that some non-uniform samples in training data can be tolerated, and other algorithms are not required to be adopted to remove all the non-uniform samples; by adopting a variational Bayes optimization method, not only can a determined power curve be obtained, but also a probability power curve can be obtained, and then a non-uniform sample in data can be identified by utilizing the probability power curve; the wind power curve fitting method only needs to set some initialization parameters, does not have any parameters to be optimized, is simple, high in precision and small in error, and can further improve the precision of wind power forecasting.
Drawings
FIG. 1 is a flow chart of a wind power curve fitting method based on infinite mixed Gaussian and spline regression according to the present invention;
FIG. 2 is a graph of raw wind speed and power data in an embodiment of the present invention;
FIG. 3 is a power curve of a data set C obtained from different models according to an embodiment of the present invention;
FIG. 4 is a probability power curve for different data sets in an embodiment of the present invention.
Detailed Description
The technical solution of the present invention is further illustrated below with reference to the following embodiments and examples.
The specific implementation mode is as follows: the embodiment is a wind power curve fitting method based on infinite mixed gauss and spline regression, as shown in fig. 1, and specifically comprises the following steps:
1) data preprocessing:
drawing an empirical power curve according to actual wind speed and power data, removing obvious abnormal data, and representing a processed sample as
Figure GDA0002486166790000041
X is as describedi，yiRespectively representing wind speed and power value, and N represents the length of a training sample;
2) constructing a robust spline regression model:
constructing a robust spline regression model yi＝Zi(xi)β+eiZ of saidi(xi) Representing the input vector calculated from the spline basis, β representing the regression coefficient, eiRepresenting the regression error obeying an infinite mixture gaussian model:
Figure GDA0002486166790000042
said
Figure GDA0002486166790000051
Representing the variance of the kth Gaussian distribution, said regression coefficients β obeying a Gaussian distribution, said pikA weight value representing the k-th gaussian distribution,
Figure GDA0002486166790000052
and pikIs about
Figure GDA0002486166790000053
Is expressed as
Figure GDA0002486166790000054
Said parameters
Figure GDA0002486166790000055
Is a variable satisfying a Beta distribution with a parameter v
Figure GDA0002486166790000056
Figure GDA0002486166790000057
The hyperparameter v satisfies the parameter e0、f0Gamma distribution of (v ═ Gamma (v | e)0，f0) Said e is0、f0Is set to 0.0001 and updates e according to the posterior distribution of the parameters obtained by variational bayes0、f0A value of (d);
3) and (3) optimizing a robust spline regression model by using variational Bayes:
constructing a final likelihood function according to prior distribution of each parameter in the robust spline regression model in the step 2):
Figure GDA0002486166790000058
p (-) is the probability distribution of the variable;
order to
Figure GDA0002486166790000059
According to the principle of variational Bayes, the posterior distribution of all parameters in the robust spline regression model is solved,
Figure GDA00024861667900000510
the < > is an expected operation;
4) and (3) obtaining a power curve and a probability power curve:
giving a new sample (x) based on the posterior distribution of the parameters obtained in step 3)*，y*) X is said*、y*Respectively representing the unknown wind speed value and the real power to be predicted, y is deduced by the following formula*Probability distribution of (2):
Figure GDA00024861667900000511
the muβ、ΣβRespectively representing the expectation and variance, Z, in the posterior distribution of the parameter β*Expressed is the sum of the wind speed x calculated according to the spline base*Corresponding input vector, y*The predicted distribution of (a) is a Gaussian mixture model, said Z*μβIs y*The point prediction value of (1);
according to y ═ Z (x) muβObtaining a predicted power curve;
and solving a corresponding probability power curve according to the probability distribution corresponding to each predicted value.
The present invention is described in further detail below with reference to specific examples, which are provided for the purpose of illustration only and are not intended to be limiting.
The examples employ the following three data sets: data set a is from a Ningxia wind farm, which contains 10000 pairs of samples (wind speed S and corresponding wind power P). Before performing the experiment, we split the data set into 2 parts, the first 8000 samples as training samples and the remaining 2000 samples as test samples. The other two data sets (B and C) are data on two different wind turbines from the same wind farm. Data set B contains 6000 pairs of samples, with the first 5000 samples being training samples and the remaining 1000 samples being test samples. 7500 pairs of samples were included in data set C, the first 6000 samples were used as training samples and the remaining 1500 samples were used as test samples. The sample sampling frequency for the above three data sets was 10min, and the raw wind speed and power data are shown in fig. 2.
In practice, in order to reduce the influence of non-uniform samples on the power curve modeling, it is often necessary to eliminate these non-uniform sample points. However, due to the limited ability of the current algorithms for identifying non-uniform samples, we cannot guarantee that all non-uniform sample points can be culled. To simulate this situation, we first removed the non-uniform sample points in the original data using a simple method.
In data set A, samples with wind speeds greater than 10m/s and power less than 14000kW were considered to be non-uniform samples and were removed directly. In data set B, samples with wind speeds greater than 6m/s and power less than 50kW, samples with wind speeds greater than 13m/s and power less than 700kW were all considered non-uniform samples and removed. In data set C, samples in wind speeds greater than 6m/s power less than 50, wind speeds greater than 12m/s power less than 600kW were removed. The simple method can only remove obvious non-uniform samples, so that some abnormal points still exist in the processed data.
To illustrate the effectiveness of the proposed method of the present invention, we compared the following models commonly used for power curve fitting methods: four parametric models (4-parameter logistic model, 5-parameter logistic model, 6 th and 9 th polynomial regression model), one non-parametric model (spline regression model) and two learning-based models (neural network method and support vector machine). For convenience of expression, the above comparative models are abbreviated as 4-PLM, 5-PLM, 6-PRM, 9-PRM, SRM, ANN, and SVM, respectively. The model adopted by the invention is abbreviated as RSRM. To quantitatively characterize the performance of each model, two indicators are generally used, namely the Mean Absolute Error (MAE) and the Root Mean Square Error (RMSE), and the calculation formula is
Figure GDA0002486166790000071
Wherein y isi，
Figure GDA0002486166790000072
Respectively expressed as real power and predicted power.
The robust regression model-based power curve fitting method provided by the invention can tolerate some non-uniform sample points in the sample. The fitting results of the power curve fitting methods of the different models are shown in table 1, and the power curve of the data set C obtained by the power curve fitting methods of the different models is shown in fig. 3.
TABLE 1 comparison of Performance of Power Curve fitting methods based on various models
Figure GDA0002486166790000073
As can be seen from table 1, the performance of the four parametric models is relatively limited, and the performance of the two learning-based models (MLP and SVM) is substantially better than that of the parametric models. The power curve obtained by the RSRM method when the inconsistent samples exist in the data is better than that obtained by a parameter model and a model based on learning. It can also be seen from fig. 3 that the power curve of RSRM is a better fit to the raw power data.
The method provided by the invention can provide a deterministic power curve and a probabilistic power curve. We can use the probability power curve to identify non-uniform sample points in the raw data. The non-uniform sample points identified from data sets A, B and C by the simple method described above were 144, 309, and 931, respectively. With 95% confidence, 445, 401, and 1102 non-uniform samples can be identified from data sets A, B and C using the method proposed by the present invention, as shown by the probability power curves for the different data sets in FIG. 4. From the above results, it can be seen that the method of the present invention can identify more non-uniform samples.
Finally, it should be noted that: the above embodiments and examples are only for illustrating the technical solutions of the present invention, and not for limiting the same; although the present invention has been described in detail with reference to the foregoing embodiments and examples, it will be understood by those of ordinary skill in the art that: the technical solutions described in the foregoing embodiments and examples can be modified, or some of the technical features can be equivalently replaced; and such modifications or substitutions do not depart from the spirit and scope of the corresponding technical solutions of the embodiments and examples of the present invention.

Claims (1)

1. A wind power curve fitting method based on infinite mixed Gauss and spline regression is characterized by comprising the following steps:
1) data preprocessing:
drawing an empirical power curve according to actual wind speed and power data, removing obvious abnormal data, and representing a processed sample as
Figure FDA0002486166780000011
X is as describedi，yiRespectively representing wind speed and power value, and N represents the length of a training sample;
2) constructing a robust spline regression model:
constructing a robust spline regression model yi＝Zi(xi)β+eiZ of saidi(xi) Representing the input vector calculated from the spline basis, β representing the regression coefficient, eiRepresenting the regression error obeying an infinite mixture gaussian model:
Figure FDA0002486166780000012
said
Figure FDA0002486166780000013
Representing the variance of the kth Gaussian distribution, said regression coefficients β obeying a Gaussian distribution, said pikA weight value representing the k-th gaussian distribution,
Figure FDA0002486166780000014
and pikIs about
Figure FDA0002486166780000019
Is expressed as
Figure FDA0002486166780000015
Said parameters
Figure FDA0002486166780000016
Is a variable satisfying a Beta distribution with a parameter v
Figure FDA0002486166780000017
Figure FDA0002486166780000018
The hyperparameter v satisfies the parameter e0、f0Gamma distribution of (v ═ Gamma (v | e))0，f0) Said e is0、f0Is set to 0.0001 and updates e according to the posterior distribution of the parameters obtained by variational bayes0、f0A value of (d);
3) and (3) optimizing a robust spline regression model by using variational Bayes:
constructing a final likelihood function according to prior distribution of each parameter in the robust spline regression model in the step 2):
Figure FDA0002486166780000021
p (-) is the probability distribution of the variable;
order to
Figure FDA0002486166780000022
According to the principle of variational Bayes, the posterior distribution of all parameters in the robust spline regression model is solved,
Figure FDA0002486166780000023
the < > is an expected operation;
4) and (3) obtaining a power curve and a probability power curve:
giving a new sample (x) based on the posterior distribution of the parameters obtained in step 3)*，y*) X is said*、y*Respectively representing the unknown wind speed value and the real power to be predicted, y is deduced by the following formula*Probability distribution of (2):
Figure FDA0002486166780000024
the muβ、ΣβRespectively representing the expectation and variance, Z, in the posterior distribution of the parameter β*Expressed is the sum of the wind speed x calculated according to the spline base*Corresponding input vector, y*The predicted distribution of (a) is a Gaussian mixture model, said Z*μβIs y*The point prediction value of (1);
according to y ═ Z (x) muβObtaining a predicted power curve;
and solving a corresponding probability power curve according to the probability distribution corresponding to each predicted value.
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